Liquid-crystal displays (LCDs) are widely used in projection displays for large screen televisions and monitors. In these LCD-based projection systems, a high power beam of light is passed through a polarizer before being incident on a LCD panel. The LCD panel controls the polarization of the incident light pixel-by-pixel and redirects it towards the corresponding polarizer/analyzer, which then redirects light having the proper polarization to a projection lens that projects an image onto a screen.
One particularly successful LCD-based projection system is a WGP-based LCoS microdisplay system, which uses both wire grid polarizers (WGPs) and liquid crystal on silicon (LCoS) panels. This microdisplay system, which has been proven to exhibit both high resolution and high image contrast when compared to other microdisplay technologies such as transmissive liquid crystal (xLCD), digital light processor (DLP), and direct-view LCD, typically uses three or more microdisplay panels (e.g., one for each primary color band) to improve on-screen brightness.
Referring to FIG. 1, a conventional 3-panel WGP-based LCoS microdisplay system is shown. The microdisplay system includes a light source 5, which for example is a high-pressure discharge lamp, and a light rod 7. The light rod 7 homogenizes the cone of light produced by the light source 5 to ensure a spatially uniform light distribution. Optionally, the light rod 7 is a polarization conversion light pipe (PCLP) for producing linearly polarized light. A first lens 8a passes the light from the light pipe 7 to a first folding mirror 9, which directs the light to a first dichroic filter 10. The dichroic filter 10 separates out the blue light from the remaining light, and directs the blue light via second 8b and third 8c lenses, and second 17 and third 16 folding mirrors to a first LCoS display panel 20a. The remaining light, which is transmitted through the dichroic filter 10, is directed via fourth and fifth lenses 8d and 8e and a fourth folding mirror 11 to a second dichroic filter 12. The second dichroic filter 12 separates the remaining light into green and red light, the former of which is directed to a second LCoS display panel 20b and the latter of which passes to a third LCoS display panel 20c. 
Prior to reaching each LCoS display panel 20a, 20b, and 20c, the incident light first passes through a WGP 15, 14, and 13 and a trim retarder compensator 21a, 21b, and 21c, respectively. Each WGP 15, 14, and 13 is a polarizer/analyzer formed from a plurality of parallel micro-wires that transmits light having a polarization orthogonal to the direction of the parallel micro-wires and reflects light having a polarization parallel to the direction of the wires (e.g., if the polarizers are designed to pass horizontal or P-polarized light, as illustrated in FIG. 1, the micro-wires will be perpendicular to the plane of FIG. 1). Each LCoS panel 20a, 20b, and 20c alters the polarization of the linearly polarized incident light pixel-by-pixel and reflects the modulated light back to the corresponding WGP 15, 14, and 13. Since each WGP 15, 14, and 13 is orientated at approximately ±45° with respect to the principal direction of light propagation, in addition to serving as a polarizer/analyzer, each WGP 15, 13 and 14 also serves as a beamsplitter for separating the incoming light from the outgoing light by steering or deflecting the light reflected from the each LCoS panel along an output optical path orthogonal to the incoming optical path. More specifically, each WGP 15, 14, and 13 reflects S-polarized light (e.g., polarized light rotated by 90° by pixels in an ON state) to the X-cube 19. The X-cube 19 aggregates (i.e., converges) the image from each of the three color channels and, via the projection lens 18, projects the final image onto a large screen (not shown). Optionally, each color channel further includes a pre-polarizer (not shown) and/or a clean-up analyzer (not shown), which for example, may include one or more WGPs and/or dichroic sheet polarizers.
The trim retarder compensators 21a, 21b, and 21c (herein simply referred to as trim retarders), are compensating elements used to improve the contrast performance level of the microdisplay system, which is otherwise limited by the residual birefringence of the LCoS panels in the dark (e.g., off) state. In particular, each trim retarder 21a, 21b, and 21c introduces a phase retardance that cancels the retardance resulting from the inherent birefringence of the corresponding LCoS panel. The term ‘retardance’ or ‘retardation’, as used herein, refers to linear retardance magnitude as opposed to circular retardance magnitude, unless stated otherwise. Linear retardance is the difference between two orthogonal indices of refraction times the thickness of the optical element. Linear retardance causes a phase difference between two orthogonal linear polarizations, where one polarization is aligned parallel to the extra-ordinary axis of the linear retarder and the other polarization is aligned parallel to the ordinary axis of the linear retarder. In contrast, circular retardance causes a relative phase difference between right- and left-handed circular polarized light.
Linear retardance may be described as either in-plane or out-of-plane retardance. In-plane retardance, expressed as optical path length difference, refers to the difference between two orthogonal in-plane indices of refraction times the physical thickness of the optical element. Out-of-plane retardance refers to the difference of the index of refraction along the thickness direction (z direction) of the optical element and one in-plane index of refraction (or an average of in-plane indices of refraction), times the physical thickness of the optical element. Normal incidence rays in a cone bundle see only in-plane retardance, whereas off-axis rays including oblique rays (i.e. non-normal but along the principal S- and P-planes) and skew rays (i.e. non-normal and incident away from the principal S- and P-planes) experience both out-of-plane retardance and in-plane retardance. Notably, in-plane retardance is not observed for the trivial case of 90° ray angle in the birefringent medium.
In the absence of trim retarders 21a-c, the P-polarized polarized light that illuminates each microdisplay panel in the dark (off) state is slightly elliptically polarized upon reflection due to the residual birefringence of the LCoS panels 20a-c. When the elliptically polarized light, which contains both a P- and an S-component, is transmitted to the corresponding WGP 15, 14, 13, the S component is reflected to the X-cube thus allowing dark state light leakage onto the large screen and limiting the contrast of the projection system.
The use of trim retarders 21a-c improves the contrast level by providing in-plane retardance that compensates for the retardance resulting from the residual birefringence in the LCoS panels 20a-c. More specifically, the trim retarders 21a-c are oriented such that their slow axes are configured at orthogonal azimuthal alignment to the slow axes of the LCoS panels 20a-c (termed “crossed axes”), while their fast axes are configured at orthogonal azimuthal alignment to the fast axes of the LCoS panels 20a-c. The terms slow axis (SA) and fast axis (FA), as used herein, refer to the two orthogonal birefringent axes when the linear retardance is measured at normal incidence. Notably, the SA and FA locations change with off-axis illumination as well as reversing the SA/FA roles for a negative out-of-plane retardance component at a large angle of incidence.
Since the slow axes of the trim retarders 21a-c and LCoS panels 20a-c are configured at orthogonal azimuthal orientations, the role of the fast/slow axes switches from the trim retarder 21a-c to the LCoS panel 20a-c for normal incidence light. In other words, light having a specific polarization is alternately delayed more then less, or vice-versa, in the trim retarder 21a-c and the LCoS panel 20a-c, respectively. The net effect is zero relative delay for the incoming polarization, and as a result, an unchanged polarization (i.e., the output light is not elliptically polarized). The corresponding WGP 15, 14, 13 and/or optional clean-up polarizer then rejects the output light so that the dark-state panel light leakage does not appear on the screen. Since the trim retarders 21a-c do not alter significantly the throughput of the panel on-state, the resulting sequential contrast (full on/full off) is excellent.
The operating principle of each trim retarder 21a-c is further illustrated in FIG. 2, with reference to the core optics of a single-channel light engine. These core optics include a pre-polarizer 30, a WGP 31, a trim retarder 32, a vertical aligned nematic (VAN)-mode LCoS panel 33, and a clean-up polarizer (not shown). In operation, unpolarized or partial polarized light output from a prior stage illumination (not shown) is passed through the pre-polarizer 30 to obtain P-polarized light. The light is transmitted through the WGP 31 and its polarization extinction ratio is enhanced. The trim retarder 32 preconditions the incoming P-polarization beam and creates an elliptical output. Ideally, the ellipticity in the polarized light incident onto the LCoS panel 33, which is in a dark (off) state, is undone by the residual panel retardance. The reflected light, after completing a double pass through the VAN-LCoS panel 33 and the trim retarder 32, thus remains P-polarized. The remaining P-polarization component transmitted by the WGP 31 is injected back into the illumination system and is eventually lost.
As discussed above, the trim retarder 32 ideally provides an A-plate retardance that matches the in-plane retardance of the corresponding LCoS panel 33 in the off-state. In practice, however, the A-plate retardance of both the LCoS panel 33 and the trim retarder 32 tends to vary within each component due to manufacturing tolerances in device thickness and material birefringence control, as well as operational drifts (temperature, mechanical stress etc). As a result, to ensure adequate compensation it is common to provide a higher A-plate retardance in the trim retarder 32 than that exhibited by the LCoS panel 33. For example, a trim retarder with an A-plate retardance of 10 nm (at λ=550 nm) is often provided to compensate for a VAN-mode LCoS exhibiting a 2 nm A-plate retardance (at λ=550 nm).
As is known to those of skill in the art, this mismatch in A-plate value requires offsetting of the optic axis of the trim retarder 32, relative to the nominal crossed axes configuration described above. In other words, the trim retarder is ‘clocked-in’ by rotating its azimuth orientation away from the crossed-axes configuration. For example, see J. Chen, M. G. Robinson and G. D. Sharp, “General methodology for LCoS panel compensation”, SID 04, Digest, pp. 990-993, 2004. FIG. 3, which shows the relative azimuthal orientations of the LCoS panel and the trim retarder slow axes, illustrates how the higher value trim retarder is “clocked” away from the bisector of S- and P-polarization planes, in the adjacent quadrant, by an angle φ. When the slow and fast axes of the VAN-LCoS panel bisect the S- and P-polarization planes, as discussed above, when the LCoS retardance is very small (e.g., <<λ/50), and for a trim retarder A-plate retardance up to a quarterwave, the over-clocked angle, φ, is approximately given by:
  ϕ  ≈                    cos                  -          1                    ⁡              (                  [                                                    Γ                a                            ⁡                              (                LC                )                                      /                                          Γ                a                            ⁡                              (                TR                )                                              ]                )              2  where Γa(TR) is the trim retarder A-plate retardance and Γa(LC) is the LCoS A-plate retardance. Accordingly, the over-clocked angle is about 39° when the LCoS exhibits a 2 mm in-plane retardance and the trim retarder provides about 10 nm of in-plane retardance.
In addition to providing in-plane retardance, it is common for the trim retarder 32 to also provide out-of-plane retardance to increase the field of view. More specifically, it is common for trim retarders to include both an A-plate compensation component for compensating the in-plane retardance and a −C-plate compensation component, which exhibits negative birefringence, for compensating for out-of plane retardance. These full function A/−C-plate trim retarders optionally also include an O-plate component. An A-plate is a birefringent optical element having its extraordinary axis oriented parallel to the plane of the plate. A C-plate is birefringent optical element having its extraordinary axis oriented perpendicular to the plane of the plate (i.e. parallel to the direction of normally incident light). An O-plate is a birefringent optical element having its extraordinary axis (i.e., its optic axis or c-axis) oriented at an oblique angle with respect to the plane of the plate.
Some examples of materials used to form A-plate components include uniaxially stretched polymer films such as polyvinylalcohol (PVA) or polycarbonate (PC) films, uniaxially aligned films of liquid crystal polymer (LCP) material, non-tilted biaxial organic foils such as cellulose acetate, birefringent crystals, and inorganic thin films. Some materials used to form −C-plate components include discotic films and liquid crystal polymer (LCP) aligned with linear photopolymerization (LPP) technology. With regard to the latter, the layer of cholesteric LCP must have a short helical pitch (i.e., much shorter than the shortest wavelength in the operational wavelength range) and a reflection wavelength peak in the UV light range. The resulting LCP/LPP-based trim retarder has been proven to be very versatile in terms of reliability, uniformity and ease of retardance targeting, and furthermore, has been proven to provide excellent contrast compensation as well as be environmentally stable.
Also of increasing interest are trim retarders wherein the birefringence is generated from the arrangement of diffractive elements (i.e., form birefringence) rather than the molecular birefringence discussed above.
It is known that a diffraction grating, configured as thin holographic element (i.e., not a volume hologram) and having a feature size much larger than the wavelength of light used for creating the diffracted output, is approximately polarization insensitive. According to scalar diffraction theory, wherein paraxial ray propagation is assumed, the diffracted output at each mth order is calculated from:
                    sin        ⁡                  (                      θ            m                    )                    =                        m          ⁢                                          ⁢          λ                Λ              ,                  ⁢    and                      I        m            =                        (                      2                          m              ⁢                                                          ⁢              π                                )                2              ,  where λ is the wavelength of light, m is the odd order of diffraction, θ is the angle of diffraction (assuming normal incidence in air entrance and exit medium), and Λ is the grating pitch.
This intensity expression includes an implicit assumption of a transverse, phase-only binary grating. In other words, it is assumed that the grating has a modulation pattern substantially perpendicular to the device normal, that the grating is substantially lossless, and that the modulation is effected by phase encoding rather than intensity encoding. It is also assumed that the grating is regular without pixelation and dead-space effects. For cases with pixelation/dead-space (i.e., non-50% duty cycle square-wave grating) and general hologram patterns, more involved expressions are available to predict the output at each diffracted angle. For example, see K. L. Tan et al., “Dynamic holography for optical interconnections. II. Routing holograms with predictable location and intensity of each diffraction order,” J. Opt. Soc. Am. A, 18(1), pp. 205-215, 2001, hereby incorporated by reference.
If, however, the traverse diffraction grating has a feature size that is only a fraction of the wavelength of light used for creating the diffracted output, only the zeroth diffraction order will be reflected/transmitted. All other orders are evanescent (i.e., non-zero orders decay beyond some appreciable distance from the grating plane). The grating is now polarization dependent. For a one-dimensional grating, the P-plane (also TM-wave) and S-plane (TE-wave), parallel and perpendicular to the grating vector, respectively, complex amplitude transmittance/reflectance have different characteristics. Furthermore, at normal incidence, the effective refractive indices along and orthogonal to the grating vector differ non-negligibly. The grating is now a birefringent element having effective extraordinary and ordinary refractive indices. This zeroth order sub-wavelength grating (ZOG) is a form-birefringent element, wherein the index modulation (and hence phase modulation) of the grating is transversely-inhomogeneous (i.e., along the grating vector direction). A vector diffraction calculation tool (either modal-analysis or rigorous coupled-wave analysis) is required to predict the transmitted/reflected complex amplitude quantities.
Grid-structure elements, such as metallic grid polarizers, have been available for IR wavelengths and microwave frequencies for many years. The requirement that these elements are fabricated with sub-wavelength feature sizes is readily met, since these applications require the wavelength of the electromagnetic (EM) radiation to range from microns to sub-millimeters. In recent years, advances in semiconductor IC (integrated circuit) technology have made available lithography techniques that allow for transistor gate sizes less than about 90 nm to be fabricated, and thus is capable of providing the approximately 100 nm feature size required for visible band applications (i.e., ranging from approximately 400 nm to 700 nm).
Referring to FIG. 4, a simple, one-dimensional binary grid structure is shown. The transverse grid structure 100 includes three major elements: a first set of parallel lines 110 of a first material, a second set of parallel lines 120 of a second material interleaved with the first set of lines, and a substantially transparent substrate 130 on which both sets of wires are mounted. This basic surface-relief structure in available as a commercial wire-grid polarizer (e.g., by Moxtek), wherein the first set of lines is formed from evaporated Aluminum (and/or other dielectric materials) and the second set of lines are simply air gaps (e.g., a space that is created when the Al layer has been partially etched). Other optical stacks, such as anti-reflection (AR) layers commonly coated on the second surface of the substrate, are not shown. Also not shown are potential etch stop and capping layers for the grating structure.
Although a binary (rectangular) grating pattern is depicted, the transversely-inhomogeneous profile (along the x-direction) could also be saw-tooth-like (triangular), blazed, sinusoidal, trapezoidal etc. Each period of modulation includes two or more optical path length modulations along the device normal direction. This can be accomplished by creating two or more distinct materials at the same height (i.e., same physical thickness) or by combinations of material and physical layer thickness changes. Note that although the two materials/regions provide different phase delays in theory, in practice, an averaging effect results due to the fact that the light is unable to resolve the sub-wavelength pitch. The grating device is shown in a conical mount in a Right-handed XYZ coordinate system and with the incident electromagnetic radiation in plane 141 along the direction of the wavevector 140. The plane of incidence 141 makes an azimuthal angle 146 with the plane that contains the grating vector (i.e., XZ plane). The incident vector 140 is inclined at a polar angle of incidence (AOI) 147 relative to the device normal direction 145. In display applications, the azimuthal angles 146 range from 0 to 360 degrees and the polar angle 147 is given by half-cone angle. In a typical application, the cone axis of incident EM waves may or may not coincide with the device normal.
For a metallic grid polarizer, the grid device transmits a first polarization, substantially linear and parallel to the grating vector (i.e., parallel to the X-axis) and reflects a second polarization, substantially linear and parallel to the wire direction (i.e., parallel to the Y-axis or perpendicular to the grating vector). Effective medium theory (EMT) is applied to yield approximate effective ordinary index, no, and effective extraordinary index, ne, for the grid device. The zeroth-order effective indices, no0 and ne0, are given by,no0=√{square root over (f(n1)2+(1−f)(n2)2)}{square root over (f(n1)2+(1−f)(n2)2)}{square root over (f(n1)2+(1−f)(n2)2)} and ne0=1/√{square root over (f/(n1)2+(1−f)/(n2)2)}{square root over (f/(n1)2+(1−f)/(n2)2)}{square root over (f/(n1)2+(1−f)/(n2)2)},  (1)where n1 and n2 are the refractive indices of a first material and a second material, respectively, and f is the duty cycle of the width of the first material versus the grating period. The above EMT equations are applicable in the quasi-static limit, where the grating period approaches 0 width. In real applications, a set of second order EMT expressions provides a better approximation for the effective no and ne indices,
                                          n            o            ″                    =                                                                                          (                                          n                      o                      0                                        )                                    2                                +                                                                            (                                              p                        λ                                            )                                        2                                    ⁢                                                            π                      2                                        3                                    ⁢                                                                                                                                          f                            2                                                    ⁡                                                      (                                                          1                              -                              f                                                        )                                                                          2                                            ⁡                                              [                                                                                                            (                                                              n                                1                                                            )                                                        2                                                    -                                                                                    (                                                              n                                2                                                            )                                                        2                                                                          ]                                                              2                                                                        ⁢                                                  ⁢            and                          ⁢                                  ⁢                                            n              e              ″                        =                                                                                (                                          n                      e                      0                                        )                                    2                                +                                                                            (                                              p                        λ                                            )                                        2                                    ⁢                                                            π                      2                                        3                                    ⁢                                                                                                                                          f                            2                                                    ⁡                                                      (                                                          1                              -                              f                                                        )                                                                          2                                            ⁡                                              [                                                                              1                            /                                                                                          (                                                                  n                                  1                                                                )                                                            2                                                                                -                                                      1                            /                                                                                          (                                                                  n                                  2                                                                )                                                            2                                                                                                      ]                                                              2                                    ⁢                                                            (                                              n                        o                        0                                            )                                        2                                    ⁢                                                            (                                              n                        e                        0                                            )                                        6                                                                                ,                                    (        2        )            where the zeroth order effective indices, ne0 and no0, are used to further refine the second order approximate effective indices, n″e and n″o, with the information of wavelength of operation, λ, grating pitch, p and duty cycle, f.
According to EMT theory, the transversely-inhomogeneous grating is effectively a birefringent medium, with its e-wave axis, having an effective index ne, aligned parallel to the grating vector (X-axis). This is shown by the equivalent device 150 in FIG. 5. The o-wave axis 152, with an ordinary index no, is perpendicular to the e-wave axis 153, with extraordinary index ne, and is contained within YZ plane. This EMT layer has negative birefringence where ne<no. If the lamellar grating contains a dielectric grid, rather than a metal grid, the diattenuation property is substantially zero and the retardation property is substantially unity. Under this condition, an A-plate retarder having an in-plane retardance is created. The retardance for such a grating is (no−ne)h, where h is the grating layer thickness 151. This retarder is referred to as a −A-plate, meaning it is an A-plate retarder with negative birefringence. The significance of this is that the retardance profile vs. AOI along the e-wave plane shows a modest increase with AOI, rather than a weak decrease as in the case of positive A-plate elements.
In U.S. Pat. No. 6,532,111, Kurtz et al. propose a dielectric wire-grid polarizer formed from transversely-inhomogeneous non-conducting wire grid structures, wherein the etched pedestals are formed from multi-layer dielectric stacks. While this wire-grid device is suitable for visible band applications, the polarizing (diattenutation) characteristics of the wire grid are high, and as a result, this device is too reflective to be used as a trim retarder.
Dielectric grid optical retarders for achromatic, high-magnitude retardance applications have been proposed by Bokor et al (i.e., N. Bokor et al., “Achromatic phase retarder by slanted illumination of a dielectric grating with period comparable with the wavelength,” Appl. Opt. 40, (13) pp. 2076-2080, 2001). However, since the proposed device requires a high-angle conical mount and it is meant for parallel beam applications, it is not suitable for conventional LCD-based micro-display imager applications. Furthermore, a lack of −C-plate functionality renders the device particularly unsuitable for projection contrast compensation.
In US Pub. No. 20050045799, Deng et al. propose that a substantially achromatic optical retarder formed from dielectric grids can be fabricated with super-resolution lithography methods. The proposed device 200, which is depicted in FIG. 6, includes a transversely-inhomogeneous grating 210 mounted on top of an etch-stop layer 230 and capped by a cap-layer 240. The grating includes at least two profiles, 211 and 216, where each of the profiles may be a multi-layer. It is typical to leave structure 216 as spaces between the “walls” 211. These walls are the pedestals left by an etching process. The cap-layer is coated by oblique evaporation, so as not to substantially fill in the spaces between the walls. The grating 210, as well as its process-required layers 230 and 240 are mounted on a transparent substrate 220 and the external surfaces of the resulting device are coated with multi-layer AR stacks, 250 and 260. An expanded view of the grating structure 210 is depicted in FIG. 7. The grating 210 has a layer thickness, h, while the width of the walls 211 and spaces 216 are w1 and w2, respectively. The duty cycle ratio, f, is given by,f=w1/(w1+w2)  (3)Again, the EMT expressions (1) and (2) can be used to approximate the effective ordinary and extraordinary indices. The difference of these indices gives the effective birefringence, which is a negative value. While the optical retarder taught by Deng et al. has been used in a variety of optical applications, including polarizers, isolators, and AR design, it not generally suitable for LCD-based micro-display imager applications, and in particular projection applications, due to the lack of a −C-plate component and a high crossed polarization reflectance, the latter of which is due to the use of high effective in-plane birefringence.
In U.S. Pat. No. 5,196,953, Yeh et al. propose a form-birefringent optical retarder, wherein the form-birefringence arises from an axially-inhomogeneous structure rather than the transversely-inhomogeneous structure described above. The axially-inhomogeneous structure includes a first series of layers having a first refractive index which alternate with a second series of layers having a second refractive index. The values of the first and second refractive indices, as well as the thicknesses of the layers in the first and the second series, are chosen such that the structure provides −C-plate functionality. More specifically, the following conditions are created:|ΔnL|dL=|ΔnC|dC wherein Δn is the birefringence, d is the layer thickness, and subscripts ‘L’ and ‘C’ refer to the switchable LC-layer in the display panel and the dielectric form birefringent compensator, respectively. In a preferred embodiment the lower and higher index values of no and ne in the LC layer and the compensator sections are matched. Unfortunately, this approach greatly restricts the type of dielectric form birefringent compensator material for use therein, and requires accurate measurement of material constants and coating thicknesses. Furthermore, limiting the no and ne to those of the LC-layer necessitates very thick coating layers for large −C values.
In US Pub. No. 20050128391A1, which is hereby incorporated by reference, Tan et al. disclose a trim retarder wherein the form-birefringence also arises from an axially-inhomogeneous structure. More specifically, Tan et al. teach that the axially-inhomogeneous structure that provides the form-birefringence (FB) is readily combined with one or more anti-reflection (AR) coatings to provide an FBAR element with −C-plate functionality. Advantageously, since the FB exhibits negative (−C-plate) out-of plane retardance and AR coatings typically exhibit positive (+C-plate) out-of-plane retardance, both the overall reflectance and the net C retardance are conveniently tuned to meet the requirements necessary for compensating for LCoS panels and/or other polarization sensitive devices used in projection systems.
Referring to FIG. 8, the FBAR trim retarder 300 includes an A-plate element 310 and a −C-plate element 350, both of which are mounted on a transparent substrate 390. The A-plate element typically includes a molecularly birefringent layer 320, with index matching layers and/or process required layers 321 and 322. The −C-plate element includes the alternating-index multi-layer stack 360 that exhibits axially aligned form birefringence. Similarly, the −C-plate element 350 may include index matching layers 361 and 362. The entire stack 350, including the index matching layers 361 and 362, contributes to the overall −C-plate functionality and AR performance of the trim retarder 300.
Referring to FIG. 9 the axially-inhomogeneous structure 360 includes an alternating-index multi-layer stack having a first plurality of layers 370, each of which has a first index of refraction n1 and a first thickness d1, and a second plurality of layers 380, each of which has a second index of refraction n2 and a second thickness d2, alternating with the first plurality of layers 370. The duty-cycle ratio is given by,f=d1/(d1+d2).  (4)EMT equations, eq. (1) and (2) can be used to approximate the birefringence characteristics, although a matrix based thin-film calculator handles the axially-inhomogeneous, otherwise transversely homogenous, isotropic thin layers adequately.
The −C-plate form birefringent AR can be abstracted to a negative uniaxial indicatrix, as depicted in the equivalent device 350 in FIG. 10. The indicatrix is disc-like, with the e-wave axis 353 aligned parallel to the z-axis and the o-wave axis 352 aligned perpendicular to the e-wave axis and is contained in the plane of multi-layer stack.
While this full-function A/−C-plate retarder, encompassing low reflectance design, has been shown to enhance the image contrast of VAN-mode LCoS display system from several hundreds to one to several thousands to one (e.g., see K. Tan et al., “Design and characterization of a compensator for high contrast LCoS projection systems,” SID 2005, p. 1810, 2005, hereby incorporated by reference), there is still a desire to provide improved trim retarders.